AI 中文总结
研究揭示了kagome XY顶点码在特定条件下实现非传统的$\mathbb{Z}_2\times\mathbb{Z}_2\times\mathbb{Z}_2$拓扑序，并提出CSS拓扑稳定符码用于拓扑量子信息的编码和操控。
AI 中文摘要
我们研究了 kagome 晶格上由 $XY$ 六边形和三角形晶片算符以及守恒的星形算符组成的 XY 顶点码（XYTC）的量子相图。通过利用在十二边形上精确的局部 $\mathbb{Z}_2$ 对称性，我们证明在六边形晶片算符趋于无穷大的极限下，kagome XYTC 实现了 $\mathbb{Z}_2\times\mathbb{Z}_2\times\mathbb{Z}_2$ 的拓扑有序相。这种非传统的拓扑相包含 64 个准粒子 - 交换任何子 - 其在三个着色子晶格上具有受限的运动性，建立了量子维度为八。大量的拓扑超选择分量源于六个独立的 Wilson 环算符，作为涌现的一形式对称性。所得到的任何子结构比已建立的拓扑码如顶点码和颜色码更丰富。相应地，CSS 拓扑稳定符码被提出，为拓扑量子信息的编码和操控开辟了新的可能性。
英文摘要
We investigate the quantum phase diagram of the XY toric code (XYTC) on the kagome lattice consisting of $XY$ hexagonal and triangular plaquette operators and conserved star operators. We demonstrate analytically by exploiting an exact local $\mathbb{Z}_2$-symmetry on dodecagons that the kagome XYTC realizes a $\mathbb{Z}_2\times\mathbb{Z}_2\times\mathbb{Z}_2$ topologically ordered phase in the limit of large hexagonal \mbox{plaquette} operators. This unconventional topological phase involves 64 quasi-particles - Abelian anyons - with restricted mobility on three colored sublattices establishing a quantum dimension of eight. The large number of topological superselection sectors originates from six independent Wilson loop operators, acting as emergent one-form symmetries. The resulting anyon structure is richer than that of established topological codes like the toric and the color code. A corresponding CSS topological stabilizer code is formulated, opening novel possibilities for the encoding and manipulation of topological quantum information.
Comments11 pages, 6 figures
